Question

A digital voltmeter uses a 10MHz clock and has a voltage controlled generator which provides a width of $10\mu\text{s}$ per volt of unit signal. 10V of input signal would corresponds to a pulse count of}

• A. 1500
• B. 750
• C. 1000
• D. 500

Hint:

Always ensure standard scientific units (seconds and Hertz) are used to prevent errors with micro ($\mu$) and mega ($M$) prefixes:
$10^{-6} \times 10^6 = 1$. The remaining units calculate directly.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The problem describes the operation of a digital voltmeter (ramp-type or integrating-type).
An input voltage is converted into a proportional pulse width, which gates a high-frequency clock. The number of clock pulses counted during this width is the digital representation of the voltage.

Step 2: Key Formula or Approach:
- Clock Frequency: $f_{clk}$
- Clock Period: $T_{clk} = \frac{1}{f_{clk}}$
- Total Gate Width (Time Duration): $t_{gate} = \text{Voltage} \times \text{Sensitivity}$
- Pulse Count: $N = \frac{t_{gate}}{T_{clk}} = t_{gate} \times f_{clk}$

Step 3: Detailed Explanation:

• Given parameters:
Clock frequency, $f_{clk} = 10\text{ MHz} = 10^7\text{ Hz}$.
Voltage generator sensitivity, $S = 10\,\mu\text{s/V}$.
Input voltage, $V_{in} = 10\text{ V}$.

• Calculate the total gate width $t_{gate}$ for $10\text{ V}$:
\[ t_{gate} = 10\text{ V} \times 10\,\mu\text{s/V} = 100\,\mu\text{s} = 100 \times 10^{-6}\text{ s} \]

• Calculate the number of pulses $N$ during this interval:
\[ N = t_{gate} \times f_{clk} = (100 \times 10^{-6}\text{ s}) \times (10^7\text{ Hz}) \]
\[ N = 100 \times 10^1 = 1000 \]

Step 4: Final Answer:
The pulse count is $1000$, which corresponds to Option (C).